Affine lines over derivators: Properties

Abstract

In this paper we detail a number of properties of the affine line of a derivator, including a number of morphisms between $\mathbb{D}$ and ${\mathbb{A}}_{\mathbb{D}}^1$, a monoidal structure on ${\mathbb{A}}_{\mathbb{D}}^1$ if $\mathbb{D}$ is monoidal, and a universal property of ${\mathbb{A}}_{\mathbb{D}}^1$ over $\mathbb{D}$ akin to the universal property that $R[t]$ has over $R$. These results also extend naturally to affine space ${\mathbb{A}}^n$ over a derivator $\mathbb{D}$.

31 pages, comments welcome